时间加权空间中非线性非自治演化方程的极大正则性

IF 0.9 Q2 MATHEMATICS

Arabian Journal of Mathematics Pub Date : 2022-09-07 DOI:10.1007/s40065-022-00390-0

Tebbani Hossni, Achache Mahdi

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引用次数: 0

摘要

我们考虑了半线性非自治演化方程$$\begin｛aligned｝u’（t）+A（t）u（t）=F（t，u），\，t\text｛-A.e.｝，\，u（0）=u_0的最大正则性问题。\end｛aligned｝$$这里，时间相关算子A（t）与Hilbert空间\（\mathcal｛H｝）上的（时间相关的）倍半线性形式相关联。我们在形式上的最小正则性假设下，证明了时间加权\（L^2）-空间中的最大正则性结果和前一问题解的其他正则性性质，初始值（u_0）和非齐次项F。我们的结果受到边值问题的启发。

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Maximal regularity for semilinear non-autonomous evolution equations in temporally weighted spaces

We consider the problem of maximal regularity for the semilinear non-autonomous evolution equations

$$\begin{aligned} u'(t)+A(t)u(t)=F(t,u),\, t \text {-a.e.}, \, u(0)=u_0. \end{aligned}$$

Here, the time-dependent operators A(t) are associated with (time dependent) sesquilinear forms on a Hilbert space $\mathcal {H}.$ We prove the maximal regularity result in temporally weighted $L^2$-spaces and other regularity properties for the solution of the previous problem under minimal regularity assumptions on the forms, the initial value $u_0$ and the inhomogeneous term F. Our results are motivated by boundary value problems.

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来源期刊

Arabian Journal of Mathematics MATHEMATICS-

CiteScore

2.20

自引率

8.30%

发文量

审稿时长

13 weeks

期刊介绍： The Arabian Journal of Mathematics is a quarterly, peer-reviewed open access journal published under the SpringerOpen brand, covering all mainstream branches of pure and applied mathematics. Owned by King Fahd University of Petroleum and Minerals, AJM publishes carefully refereed research papers in all main-stream branches of pure and applied mathematics. Survey papers may be submitted for publication by invitation only.To be published in AJM, a paper should be a significant contribution to the mathematics literature, well-written, and of interest to a wide audience. All manuscripts will undergo a strict refereeing process; acceptance for publication is based on two positive reviews from experts in the field.Submission of a manuscript acknowledges that the manuscript is original and is not, in whole or in part, published or submitted for publication elsewhere. A copyright agreement is required before the publication of the paper.Manuscripts must be written in English. It is the author''s responsibility to make sure her/his manuscript is written in clear, unambiguous and grammatically correct language.